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 2 years ago
A food store makes a 11–pound mixture of peanuts, almonds, and raisins. The cost of peanuts is $1.50 per pound, almonds cost $3.00 per pound, and raisins cost $1.50 per pound. The mixture calls for twice as many peanuts as almonds. The total cost of the mixture is $21.00. How much of each ingredient did the store use?
3 lbs peanuts, 6 lbs almonds, 2 lbs raisins
8 lbs peanuts, 1 lb almonds, 2 lbs raisins
6 lbs peanuts, 3 lbs almonds, 2 lbs raisins
8 lbs peanuts, 2 lbs almonds, 1 lbs raisins
 2 years ago
A food store makes a 11–pound mixture of peanuts, almonds, and raisins. The cost of peanuts is $1.50 per pound, almonds cost $3.00 per pound, and raisins cost $1.50 per pound. The mixture calls for twice as many peanuts as almonds. The total cost of the mixture is $21.00. How much of each ingredient did the store use? 3 lbs peanuts, 6 lbs almonds, 2 lbs raisins 8 lbs peanuts, 1 lb almonds, 2 lbs raisins 6 lbs peanuts, 3 lbs almonds, 2 lbs raisins 8 lbs peanuts, 2 lbs almonds, 1 lbs raisins

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jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0Start off by defining variables

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0let x = amount of peanuts (in pounds), y = amount of almonds (in pounds) and z = amount of raisins (in pounds)

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0If "A food store makes a 11–pound mixture of peanuts, almonds, and raisins" then what does this mean?

MeganDarling
 2 years ago
Best ResponseYou've already chosen the best response.1That they add up to 11 pounds haha

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0good, so x y and z add to 11, which means x+y+z = 11

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0that's one equation

MeganDarling
 2 years ago
Best ResponseYou've already chosen the best response.1But then we have to factor in how much they cost..

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0We also know that "The cost of peanuts is $1.50 per pound, almonds cost $3.00 per pound, and raisins cost $1.50 per pound" So x lbs of peanuts cost 1.5x dollars, y lbs of almonds cost 3y dollars, and z lbs of raisins cost 1.5z dollars They total 1.5x + 3y + 1.5z dollars

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0this total cost is given to be $21 so 1.5x + 3y + 1.5z = 21

MeganDarling
 2 years ago
Best ResponseYou've already chosen the best response.1so like, 1.50x+3.00y+1.50=21..

MeganDarling
 2 years ago
Best ResponseYou've already chosen the best response.1Haha Okey you already said that x.x my bad

MeganDarling
 2 years ago
Best ResponseYou've already chosen the best response.11.50z* I meant btw haha. I get that indeed.

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0close, you mean to say 1.50x+3.00y+1.50z=21 but you got it

MeganDarling
 2 years ago
Best ResponseYou've already chosen the best response.1And don't forget twice the peanuts!

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0that's your 2nd equation

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0twice the peanuts as what?

MeganDarling
 2 years ago
Best ResponseYou've already chosen the best response.1it says, the recipe calls for twice as many peanuts as almonds O.o

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0good, so the equation for that is?

MeganDarling
 2 years ago
Best ResponseYou've already chosen the best response.1ermm.. I dunno lol.. x(times2y)+y+z=11 O.O I have no idea.

MeganDarling
 2 years ago
Best ResponseYou've already chosen the best response.1knew it was wrong x.x

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0Amount of peanuts = 2 times (amount of almonds)

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0y = 2 times x or just y = 2x

MeganDarling
 2 years ago
Best ResponseYou've already chosen the best response.1oh pshh I should have thought of that x.x

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0so you have these 3 equations x+y+z = 11 1.5x + 3y + 1.5z = 21 y = 2x

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0you can use them to solve for x, y and z

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0I'll get you started

MeganDarling
 2 years ago
Best ResponseYou've already chosen the best response.1Lol I can't because I'm stupid, But smart people definitely can haha

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0x+y+z = 11 x+2x+z = 11 3x+z = 11  1.5x + 3y + 1.5z = 21 1.5x + 3(2x) + 1.5z = 21 1.5x + 6x + 1.5z = 21 7.5x + 1.5z = 21

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0so after plugging in y = 2x, you now have the new system 3x+z = 11 7.5x + 1.5z = 21

MeganDarling
 2 years ago
Best ResponseYou've already chosen the best response.1O.o That all made absolutely no sense to me but it seems to for you and that's good enough for me

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0where are you lost?

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0I took x+y+z = 11 plugged in y = 2x (ie replaced every 'y' with '2x') to get x+2x+z = 11 then I combined like terms to get 3x+z = 11

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0I did the same with 1.5x + 3y + 1.5z = 21 to get 7.5x + 1.5z = 21

MeganDarling
 2 years ago
Best ResponseYou've already chosen the best response.1oh okay ! I see now, sorry it's really late and I'm super tired :/

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0so you have 3x+z = 11 7.5x + 1.5z = 21 now

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0solve the first equation for z to get this 3x+z = 11 3x+z  3x = 11  3x z = 11  3x

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0Since z = 11  3x, you can plug it into the other equation and solve for x 7.5x + 1.5z = 21 7.5x + 1.5(11  3x) = 21 Solve for x

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0oh wait, i made a variable mistake...i switched x and y one sec

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0Let me fix real quick

MeganDarling
 2 years ago
Best ResponseYou've already chosen the best response.1I was thinking that haha x) ..

MeganDarling
 2 years ago
Best ResponseYou've already chosen the best response.1uhh ? your comment disappeared .. :o

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0it should be x = 2y, not y = 2x so x+y+z = 11 2y+y+z = 11 3y + z = 11 z = 11  3y  1.5x + 3y + 1.5z = 21 1.5(2y) + 3y + 1.5z = 21 3y + 3y + 1.5z = 21 6y + 1.5z = 21 =========================== 6y + 1.5z = 21 6y + 1.5(11  3y) = 21 Solve that last equation for y

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0Solve 6y + 1.5(11  3y) = 21 for y

MeganDarling
 2 years ago
Best ResponseYou've already chosen the best response.1Aw man I have to go to bed soon I'm dead tired x.x

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0What do you get when you solve that equation for y

MeganDarling
 2 years ago
Best ResponseYou've already chosen the best response.1ergh I dunno x.x I'm brain dead

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0Then give it a break, get some sleep and you'll tackle it in the morning

MeganDarling
 2 years ago
Best ResponseYou've already chosen the best response.1Oh no I keep losing connection >.<
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